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  2. Contact mechanics - Wikipedia

    en.wikipedia.org/wiki/Contact_mechanics

    Contact mechanics is the study of the deformation of solids that touch each other at one or more points. [1] [2] A central distinction in contact mechanics is between stresses acting perpendicular to the contacting bodies' surfaces (known as normal stress) and frictional stresses acting tangentially between the surfaces (shear stress).

  3. Compatibility (mechanics) - Wikipedia

    en.wikipedia.org/wiki/Compatibility_(mechanics)

    The first step in the process is to show that this condition implies that the infinitesimal rotation tensor is uniquely defined. To do that we integrate ∇ w {\displaystyle {\boldsymbol {\nabla }}\mathbf {w} } along the path X A {\displaystyle \mathbf {X} _{A}} to X B {\displaystyle \mathbf {X} _{B}} , i.e.,

  4. Moment of inertia - Wikipedia

    en.wikipedia.org/wiki/Moment_of_inertia

    For bodies constrained to rotate in a plane, only their moment of inertia about an axis perpendicular to the plane, a scalar value, matters. For bodies free to rotate in three dimensions, their moments can be described by a symmetric 3-by-3 matrix, with a set of mutually perpendicular principal axes for which this matrix is diagonal and torques ...

  5. Euler angles - Wikipedia

    en.wikipedia.org/wiki/Euler_angles

    The axes of the original frame are denoted as x, y, z and the axes of the rotated frame as X, Y, Z.The geometrical definition (sometimes referred to as static) begins by defining the line of nodes (N) as the intersection of the planes xy and XY (it can also be defined as the common perpendicular to the axes z and Z and then written as the vector product N = z × Z).

  6. Non-uniform rational B-spline - Wikipedia

    en.wikipedia.org/wiki/Non-uniform_rational_B-spline

    Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces. It offers great flexibility and precision for handling both analytic (defined by common mathematical formulae ) and modeled shapes .

  7. Straightedge and compass construction - Wikipedia

    en.wikipedia.org/wiki/Straightedge_and_compass...

    Creating the one point or two points in the intersection of two circles (if they intersect). For example, starting with just two distinct points, we can create a line or either of two circles (in turn, using each point as centre and passing through the other point). If we draw both circles, two new points are created at their intersections.

  8. Plücker coordinates - Wikipedia

    en.wikipedia.org/wiki/Plücker_coordinates

    Then their respective planes are perpendicular to vectors a and b, and the direction of L must be perpendicular to both. Hence we may set d = a × b, which is nonzero because a, b are neither zero nor parallel (the planes being distinct and intersecting). If point x satisfies both plane equations, then it also satisfies the linear combination

  9. Poincaré half-plane model - Wikipedia

    en.wikipedia.org/wiki/Poincaré_half-plane_model

    The metric of the model on the half-plane, { , >}, is: = + ()where s measures the length along a (possibly curved) line. The straight lines in the hyperbolic plane (geodesics for this metric tensor, i.e., curves which minimize the distance) are represented in this model by circular arcs perpendicular to the x-axis (half-circles whose centers are on the x-axis) and straight vertical rays ...

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